1. Field of Invention
The present invention relates to a distance-enhancing coding method and, in particular, to a coding method that can be applied in data access on digital recording media and data transmission in digital communications.
2. Related Art
In digital communication systems, digital signals are transmitted from a transmitter to a receiver through a channel. The general interpretation of the channel includes different media. In a communication system, the channel is the medium for transmitting data, such as light, radio waves, etc, to transmit signal to different locations. In a data storage system, the channel is a storage medium, such as a hard disk drive, an optical disk, to store data and to transmit signals to different time points.
The signals at the transmitter are usually encoded by a channel encoder and a modulation code encoder and then modulated by a modulator. Through the transmission of a channel, it is demodulated by a demodulator, decoded by a modulation code decoder and a channel decoder to reach the receiver.
The essential technique in the invention is the design of modulation coding. The way the modulation codes work is to set a few system constraints according to some system requirements. A set of conversion rules is then designed according to the constraints so that the data after converting by these rules can satisfy the constraints of the system. These constraints are often descriptions of the number of consecutive code symbol 1s and the number of consecutive code symbol 0s.
The non-return to zero inversion (NRZI) method is a modulation method that modulates the code symbol 1 in a sequence into a varying potential in signals (the potential variation means changes from the potential 0 to the potential 1 or vice versa), and modulates the code symbol 0 in a sequence into a non-varying potential in signals (the non-varying potential means a potential 1 followed by another potential 1 and a potential 0 followed by another potential 0).
The run length limited (RLL) method is a coding method, which limits the number of consecutive 0s being not smaller than d and not greater than k (i.e., the limits are (d,k)). This method can ensure the normal operation of a phase locked loop (PLL). The smaller the k value is, the better the PLL operates.
The maximum transition run (MTR) method is a coding method that limits the number of consecutive potential variations being not greater than k. Under NRZI modulation, this then limits the number of consecutive code symbol 1s being not greater than k.
The MTR distance gain property is the same as the PLL, but in practice can gain a higher code rate.
The time-varying maximum transition run (TMTR) is a further modification of the MTR, which sets different constraints for the number of consecutive variations depending upon whether it starts at an odd or even position. For example, (k1,odd, k1,even)TMTR constraints mean that the number of consecutive 1s starting at an odd position is not greater than k1,odd and the number of consecutive 1s starting at an odd position is not greater than k1,even. This method can increase the minimum distance of the encoded system to an upper matched filter bound (MFB), therefore, it has the distance enhancing property.
The partial response maximum likelihood (PRML) method is a widely used coding technology in magnetic recording systems to obtain the largest recording density. This includes such methods as PR4, EPR4, EEPR4, etc.
Magnetic recording systems usually adopt the EEPR4 channel to increase the recording density. The relation between the output y and the input x is y(n)=x(n)+2x(nxe2x88x921)xe2x88x922x(nxe2x88x923)xe2x88x92x(nxe2x88x924), where x(nxe2x88x921) means the input x earlier than x(n) by one cycle. The dominated error event is xc2x1(1,xe2x88x921,1).
Optical recording systems usually adopt the PR2 and EPR2 channels to increase the recording density. Taking the PR2 as an example, the relation between the output y and the input x is y(n)=x(n)+2x(nxe2x88x921)+x(nxe2x88x922) and the dominated error event is xc2x1(1,xe2x88x921).
With reference to FIG. 1A, there are 16 cases for the dominated error event xc2x1(1,xe2x88x921) to occur in a 5-bit sequence. (The upper sequence is received as the lower sequence or vice versa, both of the error forms are xc2x1(1,xe2x88x921).) The sequence in the drawing is modulated in the NRZI method.
With reference to FIG. 1B, to prevent error events from happening, sequences with more than 3 consecutive 1s are excluded. In the 16 cases, aside from the first and the last cases the rest 14 cases have either the upper sequence or the lower sequence left at most, thus such error events will not occur. But the first and the last cases may still occur.
If (k1,odd=2, k1,even=1)TMTR constraints are set, all of the 16 cases will have either the upper sequence or the lower sequence left at most, all dominated error events will not occur.
FIG. 2A shows a finite-state transition diagram (FSTD) of the NRZI(k1,odd=2, k1,even=1)TMTR constraints. The vertex at the bottom of the diagram represent odd positions and the number of 1s starting at the odd positions can be 1 or 2, satisfying the constraint of k1,odd=2. The vertex at the top of the diagram represent even positions and the number of 1s starting at the even positions can be 1 only, satisfying the constraint of k1,even=1.
With reference to FIG. 2B, which shows a simplified FSTD with the NRZI (k1,odd=2, k1,even=1)TMTR constraints, the states are labeled from left to right as S1, S2, and S3. The state S1 travels through path 1 or path 0 to the state S2. The state travels through path 0 to the state S2 and through path 1 to the state S3. The state S3 travels through path 0 to the state S2.
With reference to FIG. 2C, which shows a transition matrix with the NRZI(k1,odd=2, k1,even=1)TMTR constraints. The entry in the ith column and jth row of the transition matrix is the number of paths for traveling from state Si to state Sj. For example, T1,1=0 means that the number of paths for traveling from state S1 to state S1 is 0; T1,2=2 means that the number of paths for traveling from state S1 to state S2 is 2. The code rate refers to the ratio of the input bits over output bits. If an m-bit input sequence is received and converted to an n-bit codeword, where m and n are positive integers and n greater than m, then the code rate is m/n. The channel capacity is defined as the upper limit of the code rate, which can be obtained by taking the logarithm of the largest eigenvalue of the transition matrix in the base of 2. The transition matrix T provided in the drawing has a channel capacity C of about 0.7925. Since C greater than xc2xe, it is possible to design a (k1,odd=2, k1,even=1)TMTR constrained code with a code rate of xc2xe; but C less than ⅘, it is thus impossible to design a (k1,odd=2, k1,even=1)TMTR constrained code with a code rate of ⅘.
With reference to FIG. 2D for 8 sets of codewords with the NRZI(k1,odd=2, k1,even=1)TMTR constraints and a code rate of xc2xe, this coding method has a coding gain of about 1.8 dB.
It is a primary object of the invention to improve existing TMTR coding methods and to provide a coding method that can keep a coding gain of 1.8 dB while raising the code rate from xc2xe to ⅘.
It is another object of the invention to provide a method for searching block codes of distance-enhancing coding that can find required block codes by following specific steps.